Q. 134.3( 247 Votes )

# As observed from the top of a 75 m high lighthouse from the sea-level, the angles of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships

Answer :

A and D are the two ships and the distance between the ships is AD. BC is the lighthouse and is the height of the lighthouse. observer is at point C

Give: BC = height of lighthouse = 75m

∠CAB = 45°,

∠CDB = 30°

To Find: DA

In Δ ABC,

[ p = perpendicular and b = base of the right angled triangle]

AB=75 m [ tan 45º = 1]

In Δ CDB,

AD + AB= 75√3 m

DA = 75( √3 - 1) m

Hence the distance between the ships is 75( √3 - 1) m

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PREVIOUSFrom the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.NEXTA 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see Fig. 9.13).Find the distance traveled by the balloon during the interval.

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